Abstract
This manuscript introduces new synchronization methods, viz., modified fractional and inverse matrices hybrid function projective difference synchronization based on active control method. The main advantage of this method lies in its comprising of different synchronization schemes applicable componentwise, thereby strengthening the anti-attack capability in secure communications. Numerical simulations have been performed on complex fractional Rikitake system, El-Nino system, and generalized Lotka Volterra systems which verify the efficacy of the designed scheme by achieving quicker synchronization. Comparison of results with some previous published results have been made and application of synchronized methods in secure communication is made.
Similar content being viewed by others
References
Butzer PL, Westphal U. An introduction to fractional calculus. In: Applications of fractional calculus in physics. World Scientific; 2000. p. 1–85.
Das S, Yadav VK. Stability analysis, chaos control of fractional order vallis and el-nino systems and their synchronization. IEEE/CAA J Autom Sin. 2017;4(1):114–24.
Dongmo ED, Ojo KS, Woafo P, Njah AN. Difference synchronization of identical and nonidentical chaotic and hyperchaotic systems of different orders using active backstep** design. J Comput Nonlinear Dyn. 2018;13(5):051005.
He J, Chen F, Lei T. Fractional matrix and inverse matrix projective synchronization methods for synchronizing the disturbed fractional-order hyperchaotic system. Math Methods Appl Sci. 2018;41(16):6907–20.
Hilfer R. Applications of fractional calculus in physics. In: Hilfer R, editor. Applications of fractional calculus in physics. World Scientific Publishing Co. Pte. Ltd.; 2000. ISBN# 9789812817747.
Jahanzaib LS, Trikha P, Baleanu D. Analysis and application using quad compound combination anti-synchronization on novel fractional-order chaotic system. Arab J Sci Eng. 2020;45:1–14
Khan A, Jahanzaib LS, Trikha P. Analysis of a novel 3-d fractional order chaotic system. In: international conference on power electronics, control and automation (ICPECA). IEEE 2019;1–6
Khan A, Jahanzaib LS, Trikha P. Changing dynamics of the first, second and third approximations of the exponential chaotic system and their application in secure communication using synchronization. Int J Appl Comput Math. 2020;7(1):1–26.
Khan A, Jahanzaib LS, Trikha P. Fractional inverse matrix projective combination synchronization with application in secure communication. In: Proceedings of international conference on artificial intelligence and applications. Springer; 2020. p. 93–101.
Khan A, Jahanzaib LS, Trikha P. Secure communication: using parallel synchronization technique on novel fractional order chaotic system. IFAC-Pap OnLine. 2020;53(1):307–12.
Khan A, Jahanzaib LS, Trikha P, Khan T. Changing dynamics of the first, second and third approximates of the exponential chaotic system and their synchronization. J Vib Test Syst Dyn. 2020;4(4):337–61.
Khan A, Trikha P. Compound difference anti-synchronization between chaotic systems of integer and fractional order. SN Appl Sci. 2019;1:1–13.
Khan A, Trikha P. Study of earth-changing polarity using compound difference synchronization. GEM Int J Geomath. 2020;11(1):7.
Khan A, Trikha P, Jahanzaib LS. Secure communication: Using synchronization on a novel fractional order chaotic system. In: 2019 international conference on power electronics, control and automation (ICPECA). IEEE; 2019. p. 1–5.
Khan A, Trikha P, Jahanzaib LS. Dislocated hybrid synchronization via. tracking control and parameter estimation methods with application. Int J Model Simul. 2020;40:1–11.
Luo AC. A theory for synchronization of dynamical systems. Commun Nonlinear Sci Numer Simul. 2009;14(5):1901–51.
Mahmoud EE, Jahanzaib LS, Trikha P, Alkinani MH. Anti-synchronized quad-compound combination among parallel systems of fractional chaotic system with application. Alex Eng J. 2020;59:4183-4200
Mahmoud EE, Trikha P, Jahanzaib LS, Almaghrabi OA. Dynamical analysis and chaos control of the fractional chaotic ecological model. Chaos Solitons Fractals. 2020;141:110348.
McMillen T. The shape and dynamics of the rikitake attractor. Nonlinear J. 1999;1:1–10.
Ojo KS, Ogunjo ST, Fuwape IA. Modified hybrid combination synchronization of chaotic fractional order systems. 2018. ar**v preprint ar**v:1809.09576.
Ouannas A, Grassi G, Wang X, Ziar T, Pham VT. Function-based hybrid synchronization types and their coexistence in non-identical fractional-order chaotic systems. Adv Differ Equ. 2018;2018(1):309.
Ouannas A, Wang X, Pham VT, Ziar T. Dynamic analysis of complex synchronization schemes between integer order and fractional order chaotic systems with different dimensions. Complexity. 2017;2017.
Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys Rev Lett. 1990;64:821–4.
Podlubny I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, vol. 198. Elsevier; 1998.
Previte JP, Paullet JE, English E, Walls Z. A Lotka–Volterra three species food chain. Math Mag. 2001;75:243–55.
Tavassoli MH, Tavassoli A, Rahimi MO. The geometric and physical interpretation of fractional order derivatives of polynomial functions. Differ Geom Dyn Syst. 2013;15:93–104.
Trikha P, Jahanzaib LS. Dynamical analysis of a novel 4-d hyper-chaotic system with one non-hyperbolic equilibrium point and application in secure communication. Int J Syst Dyn Appl (IJSDA). 2020;9(4):74–99.
Trikha P, Jahanzaib LS. Dynamical analysis of a novel 5-d hyper-chaotic system with no equilibrium point and its application in secure communication. Differ. Geom. Dyn. Syst. 2020;22.
Trikha P, Jahanzaib LS. Secure communication: using double compound-combination hybrid synchronization. In: Proceedings of international conference on artificial intelligence and applications. Springer; 2020. p. 81–91.
Vaidyanathan S. Anti-synchronization of the generalized Lotka–Volterra three-species biological systems via adaptive control. Int J PharmTech Res. 2015;8(8):141–56.
Wei Q, Wang X, Hu X. Hybrid function projective synchronization in complex dynamical networks. AIP Adv. 2014;4(2):027128.
Yadav VK, Srikanth N, Das S. Dual function projective synchronization of fractional order complex chaotic systems. Opt Int J Light Electron Opt. 2016;127(22):10527–38.
Zhang H, Liu D, Wang Z. Controlling chaos: suppression, synchronization and chaotification. Berlin: Springer Science & Business Media; 2009.
Zhang Q, **ao J, Zhang XQ, Cao D. Dual projective synchronization between integer-order and fractional-order chaotic systems. Opt Int J Light Electron Opt. 2017;141:90–8.
Acknowledgements
The second author is funded by the Senior Research Fellowship of the Council of Scientific and Industrial Research,India HRDG (CSIR) sanction letter no. 09/466(0189)/2017-EMR-I.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Khan, A., Trikha, P. & Khan, T. Secure Communication Using Modified Fractional and Inverse Matrices Synchronization Methods. SN COMPUT. SCI. 2, 91 (2021). https://doi.org/10.1007/s42979-021-00481-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s42979-021-00481-3